Spatial functions approximation by Boolean arrays

Since Cellular Automata attract a growing interest as a model to be used in simulating spatial dynamics, the problem arises of Boolean data compatibility with continuous spatial functions widespread in physics. To solve this problem, a method to approximate real functions in discrete space by Boolean arrays and vice versa is proposed. The approximation errors are assessed, and techniques of decreasing them are considered. Arithmetic operations in the domain of Boolean and real arrays are considered.